The St.Joe Company grows pine trees and the average annual increase in tree diameter is 3.1 inches with a standard deviation of 0.5 inches.A random sample of n = 50 trees is collected.What is the probability of the sample mean being less the 2.9 inches?
A)0.4977
B)0.0023
C)0.9977
D)0.9954

Question

Quizplus · Accepted Answer

We need to use the central limit theorem to approximate the sampling distribution of the sample mean, which is assumed to be normal with mean=3.1 and standard deviation=0.5/sqrt(50)=0.0707.
Thus, z=(x̄-μ)/σ= (2.9-3.1)/0.0707=-2.83.
Using a standard normal table, we find P(z<-2.83)=0.0023.

The StJoe Company Grows Pine Trees and the Average Annual Increase